Probabilistic Inference in Differentially Private Systems

1. A method comprising: generating a noisy result using a differentially private computation from a private data set by a computing device, wherein the differentially private computation adds noise to the private data set using an exponential mechanism; determining a conditional distribution of the differentially private computation wherein the conditional distribution describes a probability distribution for the noisy result; determining a posterior distribution for the differentially private computation by the computing device using preexisting knowledge about one or more records of the private data set and the conditional distribution, wherein the preexisting knowledge comprises one or more of information about a user whose data is part of the private data set or information about a total number of records of the private data set; wherein determining the posterior distribution using the preexisting knowledge about the one or more records of the private data set and the conditional distribution comprises: retrieving a plurality of results from previous executions of the differentially private computation that were generated in response to previously received queries; and inferring the posterior distribution using the conditional distribution, the plurality of results, and the preexisting knowledge about the one or more records of the private data set using probabilistic inference; and providing the posterior distribution by the computing device, wherein the posterior distribution includes the probability that the generated noisy result is a true result from the private data set.

2. The method of claim 1 , further comprising providing the noisy result.

3. The method of claim 1 , wherein using probabilistic inference comprises using Markov Chain Monte Carlo methods.

4. The method of claim 1 , wherein the conditional distribution is one of a Laplacian distribution or a Gaussian distribution.

5. The method of claim 1 , wherein the differentially private computation is an exponential mechanism.

6. The method of claim 1 , wherein the private data set comprises census data.

7. The method of claim 1 , wherein the private data set comprises medical data.

8. A method comprising: receiving a noisy first result at a computing device through a network, wherein the noisy first result is generated from a second result of a private data set using a differentially private computation that adds noise to the private data set using an exponential mechanism; determining a conditional distribution of the differentially private computation by the computing device, wherein the conditional distribution of the differentially private computation describes a probability distribution for the noisy first result; retrieving a plurality of results from previous executions of the differentially private computation that were generated in response to previously received queries; probabilistically inferring a posterior distribution of the differentially private computation using the conditional distribution, the plurality of results, and preexisting knowledge about one or more records of the private data set by the computing device, wherein the preexisting knowledge comprises one or more of information about a user whose data is part of the private data set or information about a total number of records of the private data set; and providing the posterior distribution by the computing device through the network, wherein the posterior distribution includes the probability that the noisy first result is equal to the second result from the private data set.

9. The method of claim 8 , further comprising providing the noisy first result through the network.

10. The method of claim 8 , wherein probabilistically inferring the posterior distribution comprises probabilistically inferring the posterior distribution using Markov Chain Monte Carlo methods.

11. The method of claim 8 , wherein the conditional distribution is one of a Laplacian distribution or a Gaussian distribution.

12. The method of claim 8 , wherein the private data set comprises census data.

13. The method of claim 8 , wherein the private data set comprises medical data.

14. A system comprising: a computing device; a privacy integrated platform that generates a noisy first result from a second result of a private data set using a differentially private computation, wherein the differentially private computation adds noise to the private data set using an exponential mechanism; and an inference engine that: determines a conditional distribution of the differentially private computation, wherein the conditional distribution of the differentially private computation describes a probability distribution for the noisy first result; generates a posterior distribution for the differentially private computation using preexisting knowledge about one or more records of the private data set and the conditional distribution, wherein the preexisting knowledge comprises one or more of information about a user whose data is part of the private data set or information about a total number of records of the private data set, and wherein generating the posterior distribution using the preexisting knowledge about the one or more records of the private data set and the conditional distribution comprises: retrieving a plurality of results from previous executions of the differentially private computation that were generated in response to previously received queries; and inferring the posterior distribution using the conditional distribution, the plurality of results, and the preexisting knowledge about the one or more records of the private data set using probabilistic inference; receives the generated noisy first result; and provides the generated noisy first result and the generated posterior distribution, wherein the posterior distribution includes the probability that the generated noisy first result is equal to the second result from the private data set.

15. The system of claim 14 , wherein the differentially private computation is an exponential mechanism.

16. The system of claim 14 , wherein the conditional distribution is one of a Laplacian distribution or a Gaussian distribution.